High quality extra-virgin olive oils are perfect for salads or drizzling over cooked food, but they're also expensive. When you're cooking with oil, food author Molly Stevens suggests saving your fancy olive oil — the cheap stuff will do just as well.
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In her excellent book All About Braising: The Art of Uncomplicated Cooking, Stevens explains:
[T] he best-quality, highest-priced, estate-bottled extra-virgin olive oils, especially any nonfiltered oils, should indeed not be used for cooking. First, the flavor and character will fade as you heat the oil, and if you've paid a hefty sum, it's a waste to pour it into a sauté pan. Second, any particles left in an unfiltered oil (as many of the best are) will burn and deteriorate when heated, and thus add bitterness to your recipes. Save these for drizzling over a plate of sliced summer tomatoes... or a hunk of rustic bread.
In short: Go with the inexpensive extra virgin olive oil for cooking. Lifehacker HQ Los Angeles is using Stevens's book to braise a tasty holiday meal, but the book is full of other useful tips along these lines in the An Opinionated Pantry chapter — definitely worth checking out if you're into food.